BANDUNG, fmipa.itb.ac.id. -Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, in collaboration with Pusat Kolaborasi Riset Teori Graf dan Kombinatorika Indonesia (Center for Indonesian Graph Theory and Combinatorics Research Collaboration) held again regular monthly activities in the form of the 2023 Combinatorics Today Series or commonly abbreviated as the 2023 CTS. Throughout the year 2023, which is the third year that CTS has been running, there will be 11 editions of CTS featuring leading speakers in the fields of graph theory and combinatorics from various countries, including Australia, the Czech Republic, Italy, the Philippines, Austria, Slovenia, Canada, and Indonesia is no exception.
In the fourth edition of the 2023 CTS, Thursday, June 8, 2023 at 14.00-15.30 WIB, Prof. Gordon Royle from the University of Western Australia (UWA) gave a lecture entitled Hamilton Cycles in Cubic and Other Graphs. A Hamilton cycle in a graph G=(V,E) is defined as a cycle that passes through each vertex v ϵ V exactly once each. The history of naming the Hamilton cycle begins with a game invented by Sir William Rowan Hamilton. This game is called the Icosian game, where players are asked to find a cycle that passes through each point of a dodecahedron graph exactly once. The scientific study of the Hamilton cycle is motivated by the famous Four Color Theorem. More than a century of research has produced a large body of literature examining the existence and calculation of Hamiltonian cycles, but, according to Royle, it still leaves fundamental questions and interesting conjectures unresolved.
Prof. Gordon Royle presented several results and problems related to graphs that are uniquely Hamiltonian (UH), that is, they have exactly one Hamiltonian cycle. Tutte showed that no 3-regular graph is uniquely Hamiltonian, and it was long suggested by Sheehan (1975) in his conjecture that a similar result holds for 4-regular graphs. In his riveting presentation, Prof. Royle also presented several computational results on the number of Hamilton cycles in various sub-families of cubic graphs, then concluded which cubic graphs had the most or the fewest Hamilton cycles.
Prof. Kiki Sugeng, as moderator for this session, said that Prof. Royle is one of the leading figures in combinatorics. Royle earned his Ph.D. in 1987, under the supervision of Cheryl Praeger and Brendan McKay with the dissertation entitled “Constructive Enumeration of Graphs”. He then spent two years at the University of Waterloo, Canada, and met Ron Read who sparked his interest in chromatic polynomials, and Chris Godsil who introduced him to algebraic graph theory. After two years at Vanderbilt University, he returned to UWA and spent 17 years in the Department of Computer Science before moving to the Department of Mathematics and Statistics in 2008. He is currently a professor in the School of Physics, Mathematics and Computation, Mathematics and Statistics at UWA. Prof. Kiki stated that Prof. Royle is the author of the famous book entitled Algebraic Graph Theory together with Chris Godsil. He was the recipient of the Gavin Brown Prize for outstanding research in combinatorics in 2010. His research interests involve using computers to generate catalogs of combinatorial objects such as cubic graphs, transitive graphs, permutation groups, finite geometries, and matroids. He has made significant contributions in the fields of graph theory, algebraic graph theory, and computational science. Since 1987, he has written more than 60 articles and has been cited more than 500 times.
As usual, every CTS edition is opened directly by Prof. Edy Tri Baskoro as Chair of the 2023 CTS Committee. In his speech, Prof. Edy, who is also Head of Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences (FMIPA), Institut Teknologi Bandung (ITB), said that holding this CTS was a commitment from Combinatorial Mathematics Research Group, FMIPA ITB, to continue to exist in the context of scientific development of graph theory and combinatorics, and to continue trying to expand research collaboration with various world centers of excellence. This webinar was attended by around 45 participants consisting of lecturers, researchers, and undergraduate and graduate students from ITB Indonesia, as well as from other universities abroad. Further information regarding CTS can be accessed via https://fmipa.itb.ac.id/combinatorics-today-series-2023/.

Next Speaker Schedule on the 2023 CTS:
July 7: Prof. Marien Abreu (University degli Studi della Basilicata – Potenza, Italy), August 18: Prof. M. Salman A. N. (Institut Teknologi Bandung, Indonesia), September 29: Prof. Jose Maria Balmaceda (University of the Philippines Diliman, Philippines), October 20: Prof. Mihyun Kang (Graz University of Technology, Austria), November 3: Prof. Kiki Ariyanti Sugeng (University of Indonesia, Indonesia), November 17: Prof. Sandi Klavzar (University of Ljubljana, Slovenia), December 8: Prof. Vida Dujmovic (University of Ottawa, Canada).